Question

Consider the probability that more than 70 out of 119 CDs will be defective. Assume the probability that a given CD will be defective is 4%. Specify whether the normal curve can be used as an approximation to the binomial probability by verifying the necessary conditions.

Answer 1

Answer: No, the normal curve cannot be used.

Step-by-step explanation:

The theorem of the Normal approximation states that if X is B(n,p) then for large n X is N(np, np(1-p)).

The accuracy of this approximation is good

i. for n > [10/p(1-p)]

ii. p is close to 1/2

Hence given p= 4% = 0.04,

q = 1 - 0.04 = 0.96

Let N = [10/p(1-p)]

We find N = 10/p(1-p) = 10/(0.04× 0.96)

N ~= 260

Since n < 260 and p < 0.5

The approximation is not a good one